Multi Plicatiox

a b c Thus,— ; because a b multipli a b ed by c gives a b c.

If we first divide by a, and then by a b c b, the result will be same ; for — b a b c c, and — =c, as before. a Hence, any power of a quantity is divi ded by any other power of the same quan tity, by subtracting the index of the divi sor from the index of the dividend.

a5 a5 1 an, Thus, LT=a.;(1-3=r-I-3=a'" 3 ; 701 am—c If only a part of the product which forms the divisor be sontained in the divi dend, the quantities contained both in the divisor and dividend must be expunged. Thus, 15 a3 6' c divided by — 3 a' 6 .r, 15 a3 62 c — 5 a b e. _.=...fire.—cy= First, divide by — 3 a3 6, and the quo tient is — 5a b c ; this quantity is still to be divided by y, and as y is not contained in it, the division can only be represented a b e is the in the usual way; that is, quotient If the dividend consist of several terms, and the divisor be a simple quantity, eve ry term of the dividend must be divided by it Thus,a3 —5 a 6 23 + 6 a 24 a3 — a .z-3 5 6 x+6 When the divisor also consists of seve ral terms, arrange both the divisor and di vidend according to the powers of some one letter contained in them ; then find how often the first term of the divisor is contained in the first term of the dividend, and write down this quantity for the first term in the quotient multiply- the whole divisor by- it, subtract the product from the dividend, and bring down to the re mainder as many other terms of the divi dend as the case may require, and repeat the operation till all the terms are brought down.

Ex. 1. If a' — 2 46+63 be divided by — b, the operation will be as follows: a — bia3 — 2 a — 6a' — a b — a 6+6' — a b+61 • •The reason of this and the foregoing rule, is, that as the whole dividend is made up of all its parts, the divisor is contained in the whole,as oftcn as it is contained in all the parts. In the preceding operation we inquire, first, how often a is contained in a3, which gives a for the first term of the quotient, then multiplying the whole divisor bv it, we have a3 b to be sub tracted from the dividend, and the re mainder is — a b+6', with which we are to proceed as before.

The whole quantity a' — 2 a is in reality divided into two parts by the pro cess, each of which is divided by a — 6 ; therefore the true quotient is obtained.

Ex. 2 a+b)a d-I-6 e-ro a(e+d c-Fb ad-Fbd a di-b d • • — Ex. 3.

Remainder 1 — ±x -fx ±gr' +a' —x3 -I-x3 A-s3 — 34 +34 &c.

Ex. 4. Y-1 )Y3 —1( e+Y-1-1 -1-Y1 1 y-1 • — Ex. 5.

x—a )x3-13.34 qx—r( X2+ qx3--cia" a--p_24—a4—pa.x Remainder a —pa'±ya—r